Technique for Aggregating an Energy Service

1. A method for aggregating an energy service from a number of participants for use by a power-system operator, comprising: estimating, by a computer, a probe price to elicit energy service from one or more participants; providing the probe price to a respective participant in a group of participants; receiving, from the respective participant, a supply-function approximation that includes a slope, α, and an intercept, β, to map a price of the energy service to a supply amount that the respective participant can provide; calculating, by the computer, a purchase price, λ, for the group of participants of the energy service using the function: λ = C - ∑ i = 1 N cons ⁢ ⁢ α i ∑ i = 1 N cons ⁢ ⁢ β i , wherein C indicates a total supply quantity, and i iterates over N participants in the group of participants; responsive to the purchase price not being approximately equal to the probe price: sending, to a respective participant, an updated probe price that includes the purchase price; receiving an updated supply function approximation from the respective participant; and recalculating the purchase price using the updated supply function approximation; and responsive to the purchase price being approximately equal to the probe price, providing the purchase price to the participants.

2. The method of claim 1 , further comprising providing a bid to the power-system operator to provide the desired amount of energy service at a contracted time in the future.

3. The method of claim 2 , wherein the operations of providing the probe price, receiving the supply-function approximations, and generating the purchase price occur after the bid and before the contracted time.

4. The method of claim 1 , wherein determining whether the purchase price approximately equals the probe price includes determining whether the purchase price meets restrictions included in the supply-function approximation.

5. The method of claim 1 , wherein the purchase price is a minimum price in a range of prices.

6. The method of claim 1 , wherein the energy service includes at least one of: a demand response in which the participants agree to reduce energy demand, a commitment by the participants to provide power, and a commitment by the participants to provide ancillary power services.

7. The method of claim 1 , wherein aggregating the energy service facilitates regulation of a power system by the power-system operator.

8. The method of claim 7 , wherein the regulation occurs over a time interval that is less than 15 seconds.

9. The method of claim 1 , wherein aggregating the energy service facilitates load following in a power system by the power-system operator.

10. The method of claim 9 , wherein the load following occurs over a time interval that is less than one minute.

11. The method of claim 1 , wherein generating the purchase price involves performing Newton's method based at least in part on the supply-function approximation.

12. The method of claim 1 , wherein, after generation of the purchase price, the purchase price is fixed for the participant, who is obliged to provide a corresponding portion of the desired amount of the energy service.

13. The method of claim 1 , wherein the supply-function approximation includes a restriction on a binding responsibility of the participant.

14. The method of claim 1 , wherein the supply-function approximation includes a tangent to the supply function at the probe price.

15. The method of claim 1 , wherein the supply-function approximation is a vector that includes a series of supply-function approximations and associated prices that facilitate calculation of purchase prices in a sequence of time intervals.

16. The method of claim 15 , wherein a dynamical model is used to compute future effects of demand responses on the participant over time.

17. The method of claim 15 , where the supply function approximations are used in a model predictive control implementation.

18. The method of claim 1 , wherein the supply-function approximation includes at least one of: a difference equation, a differential equation and a finite state machine.

19. The method of claim 1 , wherein the supply-function approximation is selected from a set of predetermined functions.

20. The method of claim 1 , further comprising coupling the energy service with other power sources or other power loads.

21. The method of claim 1 , wherein generating the purchase price further involves minimizing a cost or disutility function of the participant.

22. A computer-program product for use in conjunction with a computer system, the computer-program product comprising a non-transitory computer-readable storage medium and a computer-program mechanism embedded therein to aggregate an energy service from a number of participants for use by a power-system operator, the computer-program mechanism including: instructions for estimating a probe price to elicit energy service from one or more participants; instructions for providing the probe price to a respective participant in a group of participants; instructions for receiving, from the respective participant, a supply-function approximation that includes a slope, α, and an intercept, β, to map a price of the energy service to a supply amount that the respective participant can provide; instructions for calculating a purchase price, λ, the group of participants of the energy service using the function: λ = C - ∑ i = 1 N cons ⁢ ⁢ α i ∑ i = 1 N cons ⁢ ⁢ β i , wherein C indicates a total supply quantity, and i iterates over N participants in the group of participants; instructions for recalculating the purchase price responsive to the purchase price not being approximately equal to the probe price, wherein recalculating the purchase price involves: sending, to a respective participant, an updated probe price that includes the purchase price; receiving an updated supply function approximation from the respective participant; and recalculating the purchase price using the updated supply function approximation; and instructions for providing the purchase price to the participants responsive to the purchase price being approximately equal to the probe price.

23. A computer system, comprising: a processor; memory; and a program module, wherein the program module is stored in the memory and configured to be executed by the processor, the program module to aggregate an energy service from a number of participants for use by a power-system operator, the program module including: instructions for estimating a probe price to elicit energy service from one or more participants; instructions for providing the probe price to a respective participant in a group of participants; instructions for receiving, from the respective participant, a supply-function approximation that includes a slope, α, and an intercept, β, to map a price of the energy service to a supply amount that the respective participant can provide; instructions for calculating a purchase price, λ, for the group of participants of the energy service using the function: λ = C - ∑ i = 1 N cons ⁢ ⁢ α i ∑ i = 1 N cons ⁢ ⁢ β i , wherein C indicates a total supply quantity, and i iterates over N participants in the group of participants; instructions for recalculating the purchase price responsive to the purchase price not being approximately equal to the probe price, wherein recalculating the purchase price involves: sending, to a respective participant, an updated probe price that includes the purchase price; receiving an updated supply function approximation from the respective participant; and recalculating the purchase price using the updated supply function approximation; and instructions for providing the purchase price to the participants responsive to the purchase price being approximately equal to the probe price.